$\color{#047C91}{\text{Exercise}}$: What is $k$ in the figure above? What is $n$? What is $N$?
$\color{#EF5645}{\text{Notations}}$:
$\color{#EF5645}{\text{Goal (Math)}}$: Find $c_i$ and $z_j$ to minimize $J^{clust} = \frac{1}{N}\sum_{i=1}^N ||x_i - z_{c_i}||^2$ , i.e. the mean square distance from vectors to their representatives.
Alternate between:
Such that the objective $J^{clust}$ decreases at each step.
$\color{#EF5645}{\text{Remarks}}$:
$\color{#EF5645}{\text{Recommendation}}$:
Explore first 3 clusters.